How long do hard boiled eggs stay fresh peeled? Unpeeled?

Unpeeled and in the fridge - a week. I've never kept them peeled and would think they would dry out quickly (but maybe an airtight container? with some damp paper towels?). And if you decide to pickle them -- they should keep just about forever ...

And, despite the guidance above -- if you don't like how they look or smell, throw them out. Anything that doesn't 100% pass the sniff test needs to be discarded immediately.

This is an interesting question. I travel a lot. Frequently one of the items on the hotel's "complimentary" breakfast turns out to be pre-peeled hard cooked eggs. Now I know nobody on site is going to be cooking and peeling 50 or 60 eggs each morning. So they come refrigerated from a supplier to the hotel chain. I agree with ChefOno that eggs are one of nature's miracles. I figure your own soul is shaped like an egg.